Question

Fie nr a=√7-√2 si b=√7+√2

a) calculati valoarea nr (a-b)(a-b)

b) calculati valoarea nr (a-b+2√2) la puterea 2014

Answer 1

a)(a-b)(a-b)=(a-b)²=(√7-√2)²-2(√7-√2)(√7+√2)+(√7+√2)²=
(√7-√2)²=(√7)²-2√14+(√2)²=7-2√14+2=9-2√14

(a-b)²=9-2√14-2(7-2)+9+2√14=18-2*5=18-10=8

(a-b+2√2)²°¹⁴=(√7-√2-√7-√2+2√2)²°¹⁴=0²°¹⁴=1